Topology podcasts

Mathematician Maggie Miller of the University of Texas at Austin joins Janna Levin and Steven Strogatz to explore knots, surfaces and four-dimensional topology. They discuss why loops can untangle in four spatial dimensions while two-dimensional surfaces can remain knotted, how three-dimensional snapshots help visualize 4D spaces, and Miller and collaborators’ resolution of a knotted-surface question posed by Charles Livingston in 1982. The conversation also connects visual techniques from art with mathematical reasoning.

Hosted by Janna Levin, Steven Strogatz

Michael Hill explains how topological data analysis extracts structural information from large datasets. Ideas about connectedness, holes and shape, traditionally associated with pure mathematics, provide tools for recognising patterns as the scale of analysis changes. The discussion explores applications including breast-cancer research and questions about fair voting.

Zhouli Xu explains the Kervaire invariant problem and the role of unusual geometric objects in high-dimensional topology. He describes the long route towards resolving the problem in dimension 126, including the collaborative and technical challenges behind the proof. The conversation was recorded during the Isaac Newton Institute programme on equivariant homotopy theory.

Heather Harrington explains topological data analysis and the construction of barcodes that summarize the shape of a dataset across scales. She describes how these tools reveal structure in complex information and how they can support studies of proteins and diseases such as cancer. The interview was recorded at the European Congress of Mathematics.

Carina Curto explains applications of topology to neural recordings and discusses mathematical models of recurrent networks.

Carina Curto discusses topology and mathematically tractable models of neural networks. The conversation connects population-level neural geometry with combinatorial linear-threshold networks, examining how graph structure constrains dynamics, how motifs retain properties inside larger systems, and why simpler models may help reveal principles obscured in large neural simulations.

Hosted by Paul Middlebrooks

Steven Strogatz talks with mathematicians Colin Adams and Lisa Piccirillo about knot theory and why it matters across mathematics and science. They explore how mathematicians distinguish knots, connections with the geometry of three-dimensional and higher-dimensional spaces, and applications involving DNA, materials and theoretical physics.

Hosted by Steven Strogatz